In this research a general model to study the vibration behavior of axially moving two-dimensional continuums in the presence of curvature along the moving axis is developed. To this end, an axially moving doubly-curved panel of variable radius of curvature is considered. The integral boundary value problem is obtained based on a higher-order shear deformation with first-order thickness stretching theory. Due to its high accuracy and computational performance, spectral Chebyshev approach is used to numerically solve the boundary value problem. Considering the geometry capabilities of the developed model, dynamics of various axially moving structures such as flat, singly- and doubly-curved plates/shells in different engineering applications with different boundary conditions can be investigated. The numerical results confirmed that the calculated natural frequencies for axially moving flat plates and circular cylindrical shells are in excellent agreement to those found in the literature and obtained via finite element approach. Furthermore, the effects of the axial velocity, thickness stretching, curvature ratio, and boundary conditions on the natural frequencies and stability behavior of the doubly-curved panels are investigated.

在这项研究中，建立了一个通用模型来研究在沿运动轴存在曲率的情况下轴向运动的二维连续体的振动行为。为此，考虑了具有可变曲率半径的轴向移动的双弯曲面板。基于一阶厚度拉伸理论，基于高阶剪切变形获得积分边值问题。由于其高精确度和计算性能，光谱切比雪夫方法用于数值求解边界值问题。考虑到所开发模型的几何能力，可以研究在不同工程应用中具有不同边界条件的各种轴向移动结构（如平面，单曲线和双曲线板/壳）的动力学。数值结果证实，轴向移动平板和圆柱壳的固有频率与文献中发现的并通过有限元法获得的固有频率非常吻合。此外，研究了轴向速度，厚度拉伸，曲率比和边界条件对双曲面板固有频率和稳定性行为的影响。